DISCLAIMER: this is most definitely subjective and argumentative, but I've always wanted a place to ask this question, and now finally there is one.

Also, this is one of the example questions I submitted during the definition phase, and it got upvoted quite a bit as on-topic :-)

Psychohistory looks very much like a scientific evolution of Marx's Historical Materialism: social and economic forces shape the history, and the action of single persons just can't affect so much its outcome, even if that person is the Emperor of the Galaxy himself; this is of course presented not as a mere historical analysis, but as a strong mathematical theory... nevertheless, the basic concept is pretty much the same: there are strong forces that direct the evolution of every human society, and no single action can actually divert them from their path (unless some mutant guy with psychic powers gets involved). Killing Hitler wouldn't have avoided WWII, because it was just bound to happen anyway.

But then, The End of Eternity presents the exact opposite view: every single action is important, every single moment could become the point of divergence of an alternate history; killing Hitler would have avoided WWII, or at least directed it in a very different direction.

...or maybe, we are trying to make sense of all this, while we are actually just all in the hands of Stupidity, against which, as everyone knows, "the Gods themselves fight in vain".

Back to the question: those two views of history are, of course, mutually exclusive... or are they? What did Asimov really think about this? Or was he just speculating in a direction just as in the other one? Are there other works (or other materials) from him that could clarify this issue?

7 Answers
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The statistical distribution (of a population), which affects the general trends.

The presence of outliers (such as the Mule in the Trilogy), and

Chaos theory, where small fluctuations can produce large deviations in the long term.

In the trilogy, he applied these three concepts (which are found today in sociology, anthropology, and economics) to a space empire closely based on the Roman Empire.

When it comes to your question, I don't think these facts are in contrast or opposition. Some individual actions have deep effects on future trends. These outliers, regardless if they are mutant or not, are among us. The young unemployed who set himself on fire in Tunis is such an example. Cleopatra, Caesar, Sun Tzu, Martin Luther King, Gandhi, any prophet of any religion, Jeanne d'Arc, Giordano Bruno, Galileo Galilei, Cristoforo Colombo, Gavrilo Princip, Adolf Hitler, Neil Armstrong, Mikahil Gorbachev, are all single individuals, and their actions had deep effects on the resulting history and evolution of the cultural background and events of one or more generations of people. Nevertheless, these shifts are enforced by a high-impact outlier that moves the statistical distribution towards a new center of equilibrium, potentially triggering a self-sustained positive feedback which may end up very far from the initial starting point (e.g. see the French Revolution, and the Years of Terror).

I cannot speak for Asimov, but Asimov being a scientist, his analysis of history would be rational and mathematical. His comment on "freedom of the bathroom" is indicative of this.

But the main point of Psychohistory is exactly the opposite: the actions of individuals (or small groups) just can't do anything to affect the general trends of the society...
– MassimoJan 19 '11 at 7:01

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@Massimo : that's what Seldon thinks, not Asimov, which in fact introduces the Mule as a fracture point.
– Stefano BoriniJan 19 '11 at 10:58

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These competing ideas also take form as "Great Man" vs "Great Idea" in history. The Great Man theory assumes that single people can alter the course of history. The Great Idea theory suggests that history follows the trends, and that if (for example) Hitler is killed, some other dictator will fill his place in history. The role is essential, but the actor can change. Asimov seems to explore both ideas a bit in the series.
– CodexArcanumMar 14 '11 at 20:37

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Seldon did predict that some events would cause divergences - hence the 2nd foundation of telepaths on Trantor. Seldon did not predict the Mule, because psychohistory was developed around the assumption that the only sentience in the galaxy was human. The Mule was sufficiently non-human to cause a deviation greater than the 2nd foundation could handle. We only find out later about Gaia and its influence in restoring the original path after the Mule.
– EclipseMay 15 '12 at 15:42

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Gaia doesn't restore the original path. It's said that even the Second Foundation is doomed to fail after tens of thousands of years and itself fall apart. The Gaia trend is something different.
– Brian PetersonJan 20 '14 at 11:20

I am not convinced that these two views are that divergent as such, it is more a question of scale.

On the small scale, for a particular group of people at a specific time, the actions of one person can make a big difference, can change the course of that groups history. It can effect the way that the groups develops and grows, and the place that this groups has in the wider history of its larger societal group. Even over a period of centuries, the actions of an individual can affect the group of which they are a part.

The psychohistory approach looks at a far bigger scale. It explicitly requires millions or billions of inhabited planets. It explicitly requires no real concern over which planet something happens on. So if someone had killed Hitler, it would have prevent WW2 in Europe on Earth. It may have triggered "WW2" on some other planet, or some other part of the world. Psychohistory does not apply to a group as small as the population of the Earth. If killing Hitler had prevented WW2 here but caused it on another planet the other side of the galaxy, from our perspective, that is a win. If we become the power, not them, then that is a difference for us. Even if the very large scale flow of galactic history knows no real difference.

The two concepts aren't necessarily contradictory; every action has some influence with some having more influence than others. Remember that in Eternity there's massive computing power being expended to determine exactly which action, executed when and where, will have the desired effect, and that actions may well have limited effect in the far future.

Thus killing Hitler in, say, 1937 might have prevented WW2 from happening the way it did, but this change in history may well have dampened out over the decades to follow to the point where reality in, say, 1995 would be the same except for the names in the history books and a few missing monuments.

I haven't found anything he's said about the issue, but he was a scientist. I assume, since he wrote a book on physics, that he was also familiar with the uncertainty principle, which would probably jive more with your first idea, psychohistory, since it deals mostly with probabilities.

The story is that Asimov had wasted time reading Gibbon's 'Decline and Fall of the Roman Empire" and so had nothing in mind when time came to meet with his editor Campbell so he turned the situation into a Galactic Empire and the editor loved it.

As a lover of history this gave his books real scope and weight. The idea of psycho-history is a pretty clear analogy to the gas laws in physics, where individual atoms are unknown and predictable while volumes can be described with simple laws. But he was not a determinist, throwing the Mule into the mix to mess things up! Hence the need for a second foundation, to adjust and adapt the plan as it went along.

It would be interesting to discuss if he thought about if the final second Empire was a utopia or a dystopia. In effect you have a master race ruling everyone without consent.
The fact that he never wrote a story in that time might be a clue.

The Empire in his Foundation series was based on the Chinese imperial system. Skilled people (including barbarians like Marco Polo) who could pass the civil service exams could enter the bureaucracy. This lead to a bureaucracy so massive and powerful (more powerful than the hereditary aristocracy) that the inertia would prevent even the emperor from making changes.